AP EAMCET · Maths · Hyperbola
If the eccentricity of a hyperbola is \(\sqrt{3}\); then the eccentricity of its conjugate hyperbola is :
- A \(\sqrt{2}\)
- B \(\sqrt{3}\)
- C \(\sqrt{\frac{3}{2}}\)
- D \(2 \sqrt{3}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{3}{2}}\)
Step-by-step Solution
Detailed explanation
Let \(e\) and \(e^{\prime}\) are the eccentricities of a hyperbola and its conjugate hyperbola. We know that \(\frac{1}{e^2}+\frac{1}{\left(e^{\prime}\right)^2}=1\) \(\Rightarrow \quad \frac{1}{3}+\frac{1}{\left(e^{\prime}\right)^2}=1\)…
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